The purpose of this research is to evaluate the application methodology of blended learning technology in mathematics education, with the views of teachers. In this study, the case study method, which is one of the qualitative research methods, was used. A total of 80 mathematics teachers working in various high schools in Nur Sultan city of Kazakhstan participated in the research. Research data were collected with a semi-structured interview form prepared by the researchers. As a result of the research, most of the mathematics teachers stated that the students' attitudes towards the mathematics lesson were negative. The majority of teachers participating in the research stated the combination of the superior features of face-to-face learning environments, diversity in learning and teaching methods, diversity in learning–teaching materials and increase in student success as the advantages of mathematics education in a blended learning environment. The majority of teachers participating in the research stated that the inadequacy of programmes suitable for blended learning, the deficiencies of software and hardware to be used in the course and the inability to use technology efficiently and effectively are the disadvantages of mathematics education in a blended learning environment. In-service training programmes should be organised to develop teachers' self-efficacy regarding blended learning environments and to ensure that they manage assessment and evaluation processes correctly. Keywords: Psychological and pedagogical foundations, preschool teachers, teacher competencies

The purpose of this research is to determine the proficiency levels of teachers giving computer education in high schools regarding blended learning. In this study, the competencies of teachers who give computer education in high schools regarding blended learning were handled in accordance with the survey model, which is one of the quantitative research methods. The study group of the research consists of 345 computer teachers who teach in high schools in the city of Almaty, Kazakhstan in the 2021–2022 academic year. The data of the study were collected with the blended learning proficiency scale developed by the researchers. As a result of the research, it was seen that the teachers giving computer education in high schools were high in the motivation sub-dimension of blended learning and moderate in the application sub-dimension. It has been determined that the blended learning competencies of the teachers are at a moderate level throughout the scale. Teachers’ competencies in blended learning show a significant difference according to the gender variable. As a result of the research, it was determined that the blended learning competencies of female teachers were higher than male teachers. It was concluded that teachers’ blended learning competencies did not show a significant difference according to the seniority variable. In-service training courses should be organised to increase the blended learning competencies of teachers giving computer education in high schools.   Keywords: Blended learning, learning technologies, teacher competencies;

In this study, it was aimed to determine the mobile learning readiness of university students and to examine the change according to tablet usage. The research was carried out in the fall semester of 2021–2022. The study, which was carried out with the participation of 360 university students, was carried out using the survey model. In the research, a 4-week distance education mobile learning training was given to university students. In the study, ‘Mobile Learning Readiness Scale’ was used to collect data. The scale used in the research was delivered and collected by university students online. The analysis of the data was made by using the SPSS programme, frequency analysis and t-test. The results were added to the research in the form of tables. As a result of the research, it was determined that university students have advanced mobile learning readiness. Keywords: Distance Education, Mobile Learning, Readiness, Tablet, University Students

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Today, modern Internet technologies allow you to access the necessary information at any time from anywhere. In such a situation, the ability to find what is needed from different sources and critically revise it becomes of particular importance, which, in turn, leads to the formation of basic knowledge. Consequently, when preparing young people for real life, the need to develop their critical attitude and thinking is urgent. As a rule, in real life, the initial data is not always clear, the goal is not set clearly, and there may be cases when the way out of this situation is also not the only one. Therefore, a person often faces open-type problems. Such cases can be taken as an interpretation of mathematical open problems. Indeed, open tasks are understood as tasks in which the initial data or the final goal are not clearly formulated. At the same time, students are given the freedom to set tasks to a certain extent, choose a way of thinking and enter additional parameters necessary for its solution. The article discusses plausible reasoning in the process of solving open problems and its role in the formation of students' competencies on plausible reasoning. In addition, various examples of how plausible reasoning arises when solving open problems are given, and an algorithm of actions for composing and solving open problems is given. Here the algorithm is only as an orienting basis, since there are no algorithms for solving open problems. It can be seen from the algorithm that when forming the competence of plausible reasoning, students should be able to solve closed and open problems and combine them in a certain effective sequence. Thus, it is concluded that the analysis of the compilation and solution of open mathematical problems plays an important role in the formation of the competence of plausible reasoning of future mathematics teachers and has a great influence on the preparation of young people for changing real life.